Block #193,155

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/4/2013, 8:35:49 AM · Difficulty 9.8753 · 6,634,000 confirmations

TWN

Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header

Block Hash

d9665f031306c117139b1789f7523af025c8c0f87488e7f1fecd2bd0fbfc59ae

View on Chainz ↗

Height

#193,155

Difficulty

9.875345

Transactions

Size

1.07 KB

Version

Bits

09e01697

Nonce

147,940

Timestamp

10/4/2013, 8:35:49 AM

Confirmations

6,634,000

Mined by

⛏️ P2SHANXVH8fUMzFA8pu5j6rijCgFEKvg3wbgFw

Merkle Root

a24444ca0b22c077d8c4e8decb506f814b4a2edd707da16852eaf5a31ae82f07

Transactions (5)

Coinbased0617bb6499aef…5b5d40ee2be00d

1 in → 1 out10.2800 XPM109 B

ANXVH8fU…vg3wbgFw

d68d3d1547a8bf…969aecb06a89f6

1 in → 2 out10.2300 XPM225 B

APL2XqCL…SmufnTVs AcuM7XiJ…5uND8Jce

bc8b99e2f36131…e745585a3f4302

1 in → 2 out8.1520 XPM226 B

AUhQNKNf…PQhpbWtx Abw8D7Bc…EioKVM91

dd6ec64f0f1125…98f1fca6e38452

1 in → 2 out5.2127 XPM225 B

AMZyS2P8…cqcMgvRe AG5MdEEU…3maswkU2

8fd647a4afca1c…43e1caac0bbb6b

1 in → 2 out7.6976 XPM227 B

AWMebyNT…pA783SGX AHCMBdHF…ZJLreTRk

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

4.990 × 10⁸⁷(88-digit number)

49907208332696489476…33167458899084301039

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 — Twin Prime Pair (origin ± 1)

origin − 1

4.990 × 10⁸⁷(88-digit number)

49907208332696489476…33167458899084301039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.990 × 10⁸⁷(88-digit number)

49907208332696489476…33167458899084301041

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

9.981 × 10⁸⁷(88-digit number)

99814416665392978953…66334917798168602079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.981 × 10⁸⁷(88-digit number)

99814416665392978953…66334917798168602081

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

1.996 × 10⁸⁸(89-digit number)

19962883333078595790…32669835596337204159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.996 × 10⁸⁸(89-digit number)

19962883333078595790…32669835596337204161

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

3.992 × 10⁸⁸(89-digit number)

39925766666157191581…65339671192674408319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.992 × 10⁸⁸(89-digit number)

39925766666157191581…65339671192674408321

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

7.985 × 10⁸⁸(89-digit number)

79851533332314383162…30679342385348816639

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★☆☆☆☆

Rarity

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer

Block #193,155

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